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ע⣺ՓrʯWčW 2002,21(3)305-309l
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DŽ1,2ӭ1,21,2s1,2

1  BWWϵ  B 116024

2  IbYc B 116024

ժ  Ҫ ԪֵӋĽǶȌr̅ĿɱRM˷ڿɱRԷĻA]^yIJ_벻_}ą^g˼“ϲÇrλƺ͑^yͬrRe͇ؑrģķģüs׃߶ȷԓģ@õؑ͏ģڅ^g

PI~ ^gs׃߶ȷʼģ

ЈD̖ O39TU457

1 

ݔ녢rwWʼ?Ó屾ϵHֵ͛ģƿ?/span>[1]λƵ^yƔrwԅʼؑ@Ԇ}λƷڹʽݺӋ^̵Čʩ^麆ýYͨ^õؽƷӳH̆}Ҫ[2]70ԁܵ˂ҕ[2-6]H͇ؑrԅһδ֪܉ͬr_ķЌ[3]ͬrRrԅ͵ؑM^оֵµȌλƺ͔_ӑyϢͬrݷ˿ͬrʼؑ͵،ӏԅλݷ[2][4]^AsėlͬrReԅ͵ؑ^y`^ڵIJ_ݳĎr̅Ҳ鲻_݆}|һ_}ďԓǶȌ}Mо

ԪֵӋĽǶȾͬrRrԅ͵ؑM̽ӑȻڿɱRԷĻAÅ^g˼뽨“λƺ͑^yͬr݇rģ͵ؑą^gӋģԓģԪϵyĿƷѴ׃^gyϢOӋ׃߅s\üs׃߶ȷؑ͏ģֵСֵ

2  ͬrRrģͳʼؑĿԷ

    ^rrԺD1ʾ_rλƺ͔_ӑԿˮƽP=0xʹֱQ=0ycΠͬďԿ׵λƺ͑pȥ]_ǰrwѽɵλƺ͑ஔ_߅練cؑСȵ߅rćrλƺ͑D_߅ΞD2ʾԪӋrOʼؑ_߅ϵf 0_λƺ͑ஔ_߅ϷʩӵЧĹc-f 0ćrrֵ͑[6]

               (1)

 

 

 

 

 

 

             D1    ؑµ                     D2 _ጷźd

           Fig 1  A tunnel acted by in situ stress         Fig 2  Released load due to excavation of tunnel

ʽУ Ԫκ ׺ξ rʯweʸ^rɽJ =0 ߅ =( ) Ԫĺ Ǿ_߅ІԪԪƽ̞ⷽ

                                 (2)

  c׃͑ͨ^ʽ3Ԫ׃ֵ͑ijN⻬ʩһஔڳһꇣ@

                        (3)

    ڏԾDcģ cʼؑ׃BHcԪ׺Pʽ2֪ⳣ M    cһλƷֲ Hλ^y_ģͳʼؑDzΨһֻܴ_ؑcģıֵɹʽ3Ҋһcđ׃ֵcλֵPͬӿПoME,0x,0y,0xycһ׃ֲ ʹͬrλƺ͑׃^yϢҲܸ׃Ψһڑֲ cλƷֲ ͨ^ģ “ϵɑֲ cλƷֲ Ψһ_ģ Д_ӑ^yϢrtΨһ_д׃HσHÑ^yϢ“ϲÑλ^yϢ“ϲÑ׃^yϢ_@NRĿ^yλϢrֻһ^yϢΨһ_rģ͵ؑ?‰q{õĹ۲?ԓǿ^y^y^yõҪc^yһλ^yڌʩȸߵcĿ]“ʹλƺ͑^yϢͬrReλƏģͳʼؑ

3  څ^g˼ķģ͵Ľⷽx

֪Ӌ`һֱǔֵһ^韩Ć}Դڔ`ؔ``˂ŬʹӋYҪľȃȻS}ƜyӋYijNȻʹø߾ȵ\ԱCӋYľӋ`ķeʹӋYʧȥxʩgıOyڃxȺżȻ`y׃һSCֵƵćrͳʼؑҲSC׃`^yô_ԷMзݕrݽYȻ^y`?ҾZ·ݽӌoIJ?/span>[2]

SCՓģՓͅ^gǽQ_Ԇ}N[6-7]SCՓģՓ↖}rҪ֪_ĸܶȺ`ٺH@ЩyԴ_ͨ^˞鷽ʽȡ挍طӳ^Hp˞صӰӋYĿɿ\Å^gⲻ_}@һ˼wFṩһNķ?‰qּb?ӋY^gõǰ侫_һ^g`@͞˂ܸʴ_عӋurõĽYṩһ

Å^gⲻ_}ķѽо^gcͨͬĄt\ҎtҲȫͬڃɂ^g Ąt\Ҏ飺      ^g\׌…^gUÅ^gⲻ_}rS†}ҪQαC^gŴsС[9]ֱӃMзǴ_Yϵy^gֱӃcFeMϷýYֱͬӲÅ^g\ҎtýY^g^U@Ȼ@N̎Ć}

Ѵ׃E,0x,0y,0xyһ^grزԪҪ^gą^gԽYoWʽ

                                (4)

(2)ͬʽ(4)   Dž^gꇺͅ^gԪÅ^gʾ

   

֪λƺ͑^yȵrλƺ͔_ӑ^yϢɵ

                       

           .                           (5)

ʽУ  քeǵ ^ycλֵ͵ ^yc_ӑֵ  քe^ycλ^yֵ͔_ӑ^yֵ քe^ycλ^yȺ͔_ӑ^y  քeλƺ͔_ӑ^yٿ]ڌH̆}һ㶼ܽoʽ(6)ʾĴ׃^錒ɵ½ԱC}ĽcHx

, , ,             (6)

ĶԽͬr_rԭʼؑą^gֱӃӋģͣ

                     Min / Max  

                s.t.                                                  (7)

                       

             .        

              , , ,

    ģ(7)һsļsǾԃ}IJüs׃߶ȷs׃߶ȷĵĻ˼ǵͱƽ       s׃߶ȷՔЧʸɿԺcwՔԺmһϵЃcģ(7)ļs׃߶ȷPowellͼs׃߶ȷĻAīI[11]ȡıOg߶ȾꇱȸMʩƶ

4ֵ

    ijrɣu=0.2OʼֲؑҼ0xy=00xyӷݣ^yλֵ͔_ӑ^yֵ_rģEͳʼؑ0x 0y

ֵģMrxȡһMֵ(E,0x ,0y)=(60 000, 10, 40)MPaԪMӋõDʾyՔλֵԼ^yc1 c2ˮƽ_ӷҊ1Ȼ@@4Քλֵ͔_ӑֵ^yֵ]^yxľȴ_rģE0ԭʼ0x ,0yڅ^gԪӋrڌQֻӋ낀^֞265ΆԪȡ =10 000Mpa =90 000Mpa = =2 MPa, = =60MpaӋY2ʾijһoֵڱv133΢C\Ӌrg40~70s         

  D 3    yc  

Fig 3  Allocation of observations

1 λƺ͔_ӑ^y

Table 1 Measured data of displacements and disturbed stresses

       ^ y λ                                          1           2  

      λ /10-3m                     6.0092      3.06386       -2.35280  

      x /MPa                                                                                               8.645100     11.02070

2  ReY

Table 2  Estimated results of inverse analysis

        /103MPa         0x /MPa           0y /MPa

                 60.000                              10.000                           40.000

      Reֵ(1)            59.74812~62.67481        9.33401~10.93187          38.43605~42.40228  

      Reֵ(2)            57.05523~63.10662      8.99394~11.05059            36.30976~43.00673
__________________________________________________________________________________

עReֵ(1)ָλ^yȞ10-4m_ӑ^yȞ10-2MParReY

         Reֵ(2)ָλ^yȞ10-4m_ӑ^yȞ10-1MParReY

5YZ

Å^gǴ_һNЧķԜpٽģ^е˞صӰ߷YĿɿ[10]֪^yȵrв_Ե^yÅ^gʾȻɿ^yݵąҲԓһ^g˼“ϲλƺ͔_ӑ^yϢͬr_rģͳʼؑڷM̽ӑģ(8)һЏsǾԼsļs}@}߀]ЌֵܵõȫfoһʧĽⷨHӋröͬʼcMӋ׃СֵDZҪ@дMһоһ}

 

īI

1  ĺTͥ飮rʯДֵģMPI}lչ[J]ٵVɽ199965-7

2  ֵ£r̆}ķՓč`[M]ƌW1996

3  ΐYɣrʯW}[M]ú̿I1998

4  DŽPArԭʼcԳķ[J]ľ̌W199821251-59

5  ӭDŽȣԅReݶt[J]ӋWW200018169-75

6  Gioda GBack analysis procedures for the interpretation of field measurements in geomechanics[J] Inter. J. for numerical and analytical methods in geomechanics 198711555~583

7  Rao S SBerke LAnalysis of uncertain structural systems using interval analysis[J] AIAA Journal1997354727-735

8  Elishakoff  IThree versions of the finite element method based on concepts of either stochasticity, fuzziness or anti-optimization[J]Applied Mechanics Review1998513209-218

9  cPĪȺǾԷ̽MĔֵⷨ[M]ƌW1999195-217

10  ꐑѺǴ_Yϵy^gֱӃ[J]ϾպWW1999312146-150

11  ࿡ܝOPB-2ԭ[M]hAW1997

Interval back analysis for the initial stresses and elastic modulus of the surrounding rock of tunnels

WANG Denggang1,2, LIU Yingxi1,2, LI Shouju1,2  and GANG Xianyue1,2

 (1  Dept. of Eng. Mechanics., Dalian Univ. of Technol. Dalian, 116024, China)

(2    State Key Lab. of Struct. Anal. of Ind. Equip., Dalian, 116024, China)

Abstract  The differentiability of the initial stresses and elastic constants of the surrounding rock of tunnels was discussed firstly from the view of finite element method. An interval back analysis model was put forward to identify these parameters based on the measured data of deformation and disturbed stress in the surrounding rock. The uncertain property of the measured data was considered and the interval analysis method to solve the uncertain problems was induced in the present model. The interval of the initial stresses and elastic modulus can be obtained by using the constrained variable metric method to solve the present model.

Key words  interval analysis, constrained variable metric method, initial stress field, elastic modulus 

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